How do you express intervals in inequalities such as [-2,9]?
The mathematical expressions in which both sides are not equal or balanced are called inequalities.
Answer: The two limits can be combined to give the inequality equation as -2 ≤ x ≤ 9.
Let's understand and solve
The given expression [-2,9] in the interval form is described as follows:
Square bracket '[' or ']' indicates that the extreme limits are included whereas, parenthesis '(' or ')' indicates that the extremes are not included.
Now, we have [-2,9]
x has a lower limit as -2, which is included since it has square bracket '[' attached at the lower limit but had we changed it to parenthesis i.e. '(' then -2 would not have been included.
In other words, the lower limit can be broken down into inequality "x ≥ -2" and not "x > -2" or in simpler words, it can be stated that x is greater than or equal to -2.
Next, the interval has an upper limit of 9, again 9 being included as it has square bracket ']' and not parentheses i.e ')'.
In other words, "x ≤ 9", meaning that x is less than or equal to 9.